an:06431606
Zbl 1317.60062
Puplinskait??, Donata; Surgailis, Donatas
Scaling transition for long-range dependent Gaussian random fields
EN
Stochastic Processes Appl. 125, No. 6, 2256-2271 (2015).
00343549
2015
j
60G60 60G15 60G10
stationary Gaussian random fields; scaling transition; long-range dependence; operator scaling random field
Summary: In [\textit{D. Puplinskait??} and \textit{D. Surgailis}, ``Aggregation of autoregressive random fields and anisotropic long-range dependence'', Preprint, \\url{arxiv:1303.2209v3}] we introduced the notion of scaling transition for stationary random fields \(X\) on \(\mathbb{Z}^2\) in terms of partial sums limits, or scaling limits, of \(X\) over rectangles whose sides grow at possibly different rate. The present paper establishes the existence of scaling transitions for a natural class of stationary Gaussian random fields on \(\mathbb{Z}^2\) with long-range dependence. The scaling limits of such random fields are identified and characterized by dependence properties of rectangular increments.